Method for compensating a ballistic missile for atmospheric perturbations



e ('DEGREES) Feb. 24, 1970 w. KISSINGER ETAL 3,4

METHOD FOR COMPENSATING A BALLISTIC MISSILE FOR ATMOSPHERICPERTURBATIONS Original Filed July 24, 1963 2 Sheets-Sheet 1 FEGJ.

IN VEN TOR ATTORNEY 3,497,161 METHOD FOR COMPENSATING A BALLISTIC MIS-SILE FOR ATMOSPHERIC PERTURBATIONS Charles W. Kissinger and Samuel A.Humphrey, Silver Spring, Md., assignors to the United States of Americaas represented by the Secretary of the Navy Continuation of applicationSer. No. 297,468, July 24, 1%3. This application Oct. 10, 1966, Ser. No.586,009 Int. Cl. G05d 1/10; G06f 15/50 US. Cl. 2443.2 1 Claim ABSTRACTOF THE DISCLOSURE This invention described herein may be manufacturedand used by or for the Government of the United States of America forgovernmental purposes without the payment of any royalties thereon ortherefor.

This is a continuation of application Ser. No. 297,468, filed July 24,1963, and now abandoned.

The present invention relates to the guidance of long and short rangeballistic missiles and more particularly to flight compensation of thesemissiles taking into account the eir'ects of atmospheric perturbationsthereon.

A ballistic missile as considered herein is defined as a missile whichis propelled by a thrust producing device, such as a rocket motor,during the powered stage of the flight and allowed to fly ballistically,that is without power or guidance control, during the remainder of theflight. If the power stage and the ballistic stage encounter merenominal atmospheric conditions, the missile will fly through itspredetermined programmed flight and be directed to the desired targetimpact point. However, should the atmospheric conditions producesubstantial perturbations, the missile would fly to an undesired impactpoint remote from the target and possibly outside the kill-power rangeof the missile. Such perturbations include high velocity winds,variation in density, humidity, temperature, and atmospheric pressure.

In the field of missile guidance, it has been the general practice toemploy various methods to perform the compensation of the guided missileto nullify the effect of atmospheric perturbations. One method which hasbeen employed is to provide some form of terminal guidance to providecompensation after the rocket motor stage has jettisoned. The apparatusnecessary for such terminal guidance adds to the complexity and cost ofsuch a missile and renders the missile a wholly guided missile ratherthan a ballistic missile.

Another method of nullifying the effects of the atmosphericperturbations is to measure the atmospheric perturbations prior to thelaunch of the missile and use these measurements as a basis forinserting corrections in the flight program. The thrust of the missilewhich is controlled by the flight program is terminated in accordancewith these measurements. This method requires atmospheric measurementswhich are not always possible to obtain, for example, in the case of amissile launched from a submerged submarine.

Still another method of nullifying effects of atmospheric perturbationsis to measure directly the perturb- 3,497,161 Patented Feb. 24, 1970 inginfluences, such as wind, by means of instrumentation carried by themissile as it flies through the powered stage. Internal compensationbased on these direct measurements is necessary to correct the point ofthrust termination. This method similarly introduces considerableproblems in the form of complex instrumentation, cost, and missile bornecompensation. Although such methods and devices to implement thesemethods set forth hereinabove have served the purpose, they have notproven entirely satsfactory under all conditions of service for thereasons that considerable difliculty has been experienced in obtainingthe data necessary for flight correction as well as the increasedprobability of error associated with the complex instrumentationrequired.

The general purpose of this invention is to provide a method andapparatus embracing all of the advantages similarly employed in guidancecompensation methods and devices and which produces none of theaforedescribed disadvantages. To attain, this, the present inventioncontemplates the new method of adjusting the kinematic parameters atthrust termination so that the desired target impact point is attainedin the presence of iaitmospheric perturbations occurring during themissile ight.

An object of the present invention is the provision of a new, reliablemethod of compensating for atmospheric perturbations experienced by aballistic missile during flight.

Another object of the present invention is to provide a new method ofadjusting the kinematic parameters of a ballistic missile at thrusttermination wherein no additional instrumentation, such as atmosphericcondition sensors, is required.

A further object of the present invention is the provision of a methodof compensating a ballistic missile for atmospheric perturbationswherein inertial guidance data which is already present and available inthe missile is used in determining that point of thrust terminationwhich will nullify the effects of the atmospheric perturbations.

Other objects, features and the attendant advantages of this inventionwill be readily appreciated as the same become better understood byreference to the following detailed description when considered inconnection with the accompanying drawings wherein:

FIG. 1 is a perspective drawing of the terrestial sphere showing theorientation of a missile launched from an origin at the center of thesphere and the coordinates which define the orientation of the missilefrom the point of launch to the given target;

FIG. 2 is a graphical representation of the desired pitch program of theballistic missile plotted against the distance the missile has traveledtoward the target in the range direction; and

FIG. 3 is a block diagram representation of the analog computationapparatus used to implement the method of compensation of atmosphericperturbations of the pres ent invention.

Referring now to the drawings wherein like reference charactersdesignating like or corresponding parts throughout the several views,there is shown in FIG. 1 is a ballistic missile M positioned at theorigin 0 of a terrestial sphere and coordinate system. The missile isassumed to be inertially guided during the powered stage of flight as iswell known in the missile guidance art. Kinematic parameters ordinarilyavailable and used for inertial guidance are the x, y, and z positions,the w, y, and z velocities, and b, 0, and (p, the modified Euler angles.The inertial coordinate system of FIG. 1 in which the above parametersdetermine the orientation of the missile is defined as an orthogonalright-handed system 3 having the origin at the launch point 0, the xaxis horizontal and positive in the direction extending from the originto the target T, and z axis vertical and positive in the downwardlydirection. The Euler angles 1/ 0, and (p, are referenced from theright-handed coordinate system as shown in FIG. 1. The missile isassumed to be attitude stabilized during boost, according to thefollowing error signals in azimuth and elevation, respectively;

az= 1(\ d) 2" elev. 3( d) 4q where K K K K are gain factors, yb 9 aredesired values of 1,11 and 0, q is the pitch angular rate, and r is theyaw angular rate.

The azimuth angle b,, is held at zero in the missile flight program tothereby define the direction from the origin 0 to the target T. 0 Variesthroughout the boost phase and defines a precomputed pitch program,i.e., the manner in which the missile changes pitch attitude duringboost. FIG. 2 represents one possible pitch program wherein the desiredpitch 0,, is a function of an independent variable x, the distance alongthe range line R. However, the pitch program can be based on any numberof a different independent variables such as time, at, z, 2', etc. Thefactors governing the choice of the independent variable will bediscussed in greater detail hereinafter.

It should be understood that although the discussion which is to followconcerns compensation for headwinds, tail-winds, and cross-wind type prturbations, a like consideration can be made for other types ofperturbations such as humidity changes, temperature changes, and densitychanges. Considering, for purposes of illustration, those perturbationscaused by wind perturbations, it can be seen from FIG. 1 that a windblowing cross- Wise to the direction of the flight of the ballisticmissile from origin 0 to target T will result in the development of botha y and y error. The magnitude of the errors can be used as a measure ofthe cross-wind experienced by the ballistic missile during the poweredstage. Corrective action can be taken which will reduce the cross rangeerror at impact. Such corrective action can reduce the impact errorsubstantially since the assumption can reasonably be made that the windsexperienced during the descending leg of the trajectory areapproximately the same as those experienced on the ascending leg up tothe point at which corrective action is taken. Obviously, the shorterthe range of the missile, the better this assumption becomes. Also, ifcross-wind determination occurs on the ascending leg of the trajectorybefore the maximum altitude or apogee is reached, the total wind effectwill not be detected and corrective action cannot be initiated for thosewinds which are encountered between the thrust termination and maximumaltitude. Therefore, the degree of successful compensation is enhancedwhen the boost phase or powered stage of flight covers the greatestpossible portion of the ascending leg of the trajectory.

If it is desirable to introduce the corrective action to the guidancesystem just prior to separation of the rocket motor, the amount ofchange may be expressed as follows:

Al/ld is the change in desired heading.

K 11, K K are the gain constants.

y-y is the y error existing at initiation of the corrective action, andis equal to the difference between actual displacement, y, and thedisplacement under nominal (no-wind) conditions y y'1] is the y errorexisting at initiation of the corrective action and is equal to thedifference between the actual g7 velocity and the velocity, 7 undernominal (no-wind) conditions.

By employing this method of action, the cross-wind is sensed up to thetime at which All/d is introduced. Ari/ remains fixed for the remainderof the boost stage. The value of K and K can be chosen such thateffective compensation would be obtained for essentially all of the windprofiles (i.e. the relation between altitude and wind velocity) likelyto occur on a statistical basis.

In order to compensate for impact point errors resulting from head ortail-winds as distinguished from crosswinds hereinabove considered, themissile is controlled in pitch during the boost phase in accordance withEquation 2. The variables x, 0'0, z, 2' exhibit a certain relationshipdependent upon the magnitude of the head or tail wind as the missileproceeds through the boost phase. A quite different relationship ofthese same parameters is encountered when the missile proceeds throughthe boost phase under nominal or no-wind conditions. In order to detectthe effect of such head or tail-winds by sensing changes in theseparameters it is desirable to choose both the pitch program and thefunctional relation used for detection in such a way that windperturbations are readily separable from perturbations produced by othercauses, e.g. variations in thrust, air density, launch conditions, etc.A choice of the appropriate relations to be used as a basis for themethod can best be made by using a computer which can calculatetrajectories and the effects of perturbing influences. Such a study'hasshown that a suitable mechanization is to define 0 the desired missileattitude in the vertical plane, as a function of x, as shown in FIG. 2.Winds are detected by their perturbation of the nominal relation of zversus x. For example a head or tail-wind causes the altitude z at agiven range x to be higher or lower then nominal, respectively. Ingeneral this relation may be expressed as follows:

where T nom averaged over the boost phase AT= l=variati0n of thrust fromnominal thrust,

Obviously there may be additional terms required on the right-hand sideof Equation 4 above and where significant they should be included.However, in the illustrative embodiment set forth herein only a selectnumber of terms are included. Equation 4 can be solved for Aw, thequantity which is essential in determining the desired compensation.Thrust variations which are necessary in the solution of Equation 4 maybe detected by the direct measurement of rocket motor chamber pressure,or by the effects of thrust variations on trajectory parameters. Forexample, trajectory calculations show that the function w' versus x isstrongly sensitive to variation in missile thrust and essentiallyindependent of wind. Therefore, thrust variations may be detected by thefollowing equation:

Aja 513,.

where By the determination of AT from Equation 5 and substitutionthereof into Equation 4 the measure of the wind experienced during theboost phase, Aw, is achieved. Having achieved this measure of the windexperienced during the boost phase, it is necessary to adjust the pointof thrust termination of the rocket motor and jettison thereof such thatthe desired impact point will be reached. A cut-01f criterion such asthe following will provide such a result:

AR is the actual range of the impact or target position minus thedesired range.

'R/Bx are the partial derivatives of range with respect to the indicatedvariable.

Ax is the actual value of x minus the value of x at thrust terminationunder nominal condition.

Art is the actual value of at; minus the value of a: at thrusttermination under nominal conditions.

Az is the actual value of 2 minus the value of 2 at thrust terminationunder nominal conditions.

A2? is the actual value of a minus the value of e at thrust terminationunder nominal conditions.

Aw is the wind as determined from Equation 4.

A is the variation in the air density which is equal to p 1 Pnomaveraged over the boost phase.

The mechanization and solution of Equation 6 as practiced by the presentinvention is computed by the circuitry to be set forth hereinafter inthe ballistic missile, and thrust is terminated when AR goes to zero.The partial derivatives as well as the nominal values of x, at, z, ande" must be inserted into the missile prior to launch. These quantitiescan be obtained from trajectory calculations. Aw is determined duringthe flight from Equation 4 and the remaining variable, density, can beestimated on the basis of location and season, or determined fromatmospheric pressure and temperature. Since temperature variations aremore influential than pressure variations upon the density, atemperature measurement on the missile would permit a sufiicientlyaccurate determination of density. Should the required degree ofaccuracy of wind compensation permit, an average temperature based onlocation and season could be inserted by fire control, thereby obviatingthe need for the temperature measurement device.

A schematic block diagram of one possible mechanization of the methoddescribed hereinabove is shown in FIG. 3. The computing components usedto perform the functions of integration, multiplication, summation,etc., are shown as analog type devices and are well known in the fieldof analog computation. The illustrative embodiment shown in FIG. 3 isnot necessarily optimum with regard to the number of elements required.Any details of the mechanization and instrumentation would obviouslyvary with the particular application.

The inertial reference system 10 incorporates accelerometers with astable platform and a system of free-gyros as is well known in theinertial guidance systems art. It is assumed that the output informationfor system 10 includes the angles i1 0 and and accelerations a, 7, anda.The accelerations it, 17 and a are integrated once by integrators 11, 12and 13 respectively. The output signals from the integrators 11, 12 and13 provide the velocities at, a] and a, respectively and a secondintegration by integrators 14, 15 and 16 yield the displacements x, yand z, respectively.

The inputs from fire control are derived at 17 and provide the targetrange and bearing as well as the initial conditions for integrators 11through 16. Target bearing is used to align the inertial referencesystem in azimuth, so that the azimuth angle #1 is equal to zero alongthe range line from the origin 0 to target T. Thus, the desired azimuthangle ip is maintained at zero during that portion of the boost phaseprior to the initiation of the azimuth corrective action. This isindicated at contact a of switch 18. The voltage from input 17representing target range R, drives a servo motor 19 which rotates anoutput shaft an amount proportional to the target range. This shaftdrives the potentiometers 20 through 31. Each of the individualpotentiometers of this potentiometers of this potentiometer bankprovides a variable voltage which is a non-linear function of desiredrange. The output voltages of potentiometers 20, 21, 22 and 23 representthe nominal or no-wind values of x, at, Z, and a, respectively at theprogrammed thrust termination point. This is denoted in FIG. 3 by thesubscript c/o. The differences between these nominal cut-off voltagesand the instantaneous voltages representing the instantaneous values ofx, 0'0, z and e, are obtained at summing points 32, 33, 34 and 35,respectively. The output voltages of the summing devices represent Ax,Aa'r, Az, and At which are used in the solution of Equation 6.

To obtain the first four terms of Equation 6, the terms must bemultiplied by their associated partial derivatives. With the exceptionof BR/Bx, which is always unity by definition in the coordinate systemunder consideration, these partial derivatives vary as the ballisticmissile progresses through a normal boost phase. As a first order ofapproximation, it is sufficiently accurate to use that value of thepartial derivative which applies at the point of normal boost phasecorresponding to thrust termination for the desired range. These valuesfor the derivatives m 0R d at T be E an be as functions of the desiredrange are determined by the top settings on potentiometers 25, 26 and27, respectively. It should be understood for the purposes ofillustration that these partial derivatives are less than unity and areshown as being generated by potentiometers. However, where it isnecessary to provide voltages which represent partial derivative valuesgreater than unity, an amplifier can be inserted at a convenient pointin the signal path to provide the necessary gain. This insertion of aconventional amplifier is necessary since a poten tiometer multiplies avoltage only by a factor less than unity. The first four terms ofEquation 6 thus obtained are fed to summing amplifier 36. The term isnot shown in the circuit of FIG. 3, it being assumed that this term iscomputed in fire control and entered as a correction to the desiredrange, R. Therefore, for the solution of Equation 6 it remains only tocompute the term aw Aw The manner in which this is accomplished is setforth directly hereinafter.

The output of x integrator 14 in addition to being fed to summing point32 drives a servo motor 37 which in turn drives a mechanical shaftthrough an angular rotation proportional to the value of x. Non-linearpotentiometers 38, 39 and 40 are constructed so as to generate thedesired variables as functions of x. These potentiometers aremechanically linked to the shaft being rotated by servo-motor 37. Theoutput of potentiometer 38 is the nominal value of 0; as a function of xas is required for the solution of Equation 5. The output potentiometer39 is the nominal value of z as a function of x as is required for thesolution of Equation 4. The potentiometer 40 generates the desiredelevation attitude a which is fed to summing point 41 and there comparedwith the actual elevation angle 0. The output of summing point 41 is theelevation error signal which along with the azimuth error signal derivedat summing point 42 is resolved through the roll angle by a conventionalresolver 43. The output signals of resolver 43 are values, in themissile coordinate system, for the pitch and yaw error signals which areused to control the autopilot and thereby the flight of the missile.

The Air of Equation 5 is obtained by taking the difference between theactual 5r appearing as the output of integrator 11 and the value of :rappearing as the output of nominal X potentiometer 38. This isaccomplished by the summing amplifier 44. The term AX thus obtained isdivided by EX /BT by means of potentiometer 29 to yield the quantity ATof Equation 5. This quantity AT in turn is multiplied by az /ar atpotentiometer 30 to yield the term of Equation 4. It should beunderstood that separate potentiometers 29 and 30 are shown for thepurposes of clarity and that these two potentiometers could be combinedinto one potentiometer providing the desired multiplication anddivision.

The quantity Az is obtained by taking the output z of integrator 16 andfeeding it to summing point 45 where it is compared to z the nominalvalue of 2 derived from potentiometer 39. The output be, CT

ow Aw is summed with the other terms of Equation 6 by means of summingamplifier 36 to provide the change in range AR of Equation 6.

The output voltage of amplifier 36 drives the servomotor 47 which inturn drives a mechanical shaft to thereby control the operation of theactuators 48 and 49. Actuator 48 is set to operate when AR is some valueother than zero occurring prior to thrust termination. Through theoperation of actuator 48 the contacts of switch 18 are switched from thea position to the b position. Switch 18 being a ganged switch, thepositions c and d are also controlled by switch 18. Operation ofactuator 48 to change the positions of the ganged switch, initiates theazimuth maneuver which corrects for cross range error due to cross-windsas set forth hereinabove. Prior to the time of operation of actuator 48,contact 18a is closed sending the value b to summing point 42. However,after operation of switch 48, contact 18b is closed, sending the valueAtp to summing point 42.

This value Atp is obtained by summing K and K 1] at summing amplifier 50and multiplying this sum by Ktl/ at potentiometer 24. Actuator 48 alsoserves the dual purpose of removing the 1] input from integrator 12 bybreaking contact and making contact 18d. This is necessary to insurethat A l/ remains constant throughout the azimuth maneuver.

When AR=O, actuator 49 operates thereby initiating thrust termination byproviding a separation command signal. Motor separation and thrusttermination occurs when Equation 6 is satisfied by the left-hand side,AR, being equal to zero. Ballistic flight then begins with the assurancethat compensation for the atmospheric wind perturbations has beencarried out.

Thus it may be seen by the use of purely inertial information which isalready present during the guided boost phase of a ballistic missile itis possible to detect and measure the effects of atmosphericperturbations on the flight of a ballistic missile during the poweredstage. The information thus gained is used to compensate for theseperturbations by comparing certain knownrelations of kinematicparameters for nominal atmospheric conditions to the relations of thesesame parameters under actual flight conditions. Availability of theseactual flight parameters in the inertial guidance system is therebyutilized to avoid complex instrumentation which is necessary wherecompensation of atmospheric perturbations depends upon directmeasurements thereof.

Obviously many modifications and variations of the present invention maybe made possbile in the light of the above-teachings.

What is claimed is:

1. The method of compensating an inertially guided ballistic missile foratmospheric perturbations on both the boost phase and the ballisticphase of the missile flight with a single correction at the end of theboost phase comprising the steps of:

launching the missile toward a target in a direction determined by thepredetermined trajectory parameters;

generating data signals having values corresponding to the kinematicparameters defining the predetermined trajectory of the missile undernominal atmospheric conditions;

sensing the effect of atmospheric perturbations upon the missile flightrange and bearing parameters during the boost stage of the flight;

comparing said nominal atmospheric conditions data signals with actualatmospheric conditions data signals obtained during the boost stage;

computing a range and bearing flight correction program for theballistic phase of the missile flight which doubly compensates for anydeviation between said nominal atmospheric conditions signals and actualatmospheric conditions signals at the end of the boost stage;

correcting the actual trajectory once only for the entire missile flightduring the period at the end of the boost stage to correspond with saidflight correction program; and

terminating the thrust supplied by a booster motor immediately after thecorrection of the trajectory has been introduced.

References Cited UNITED STATES PATENTS 2,932,467 4/1960 Suorgie244--3.15 3,008,668 11/1961 Darlington 2443.l4 3,164,340 1/1965 Slateret al.

3,179,355 4/1965 Pickering et al. 244-3.l4 3,188,019 6/1965 Boutin244-320 VERLIN R. PENDEGRASS, Primary Examiner

